Complementarity Framework for Nonlinear Analysis of Tensegrity Structures with Slack Cables

Abstract

A comprehensive complementarity framework is presented for both nonlinear static and dynamic analyses of tensegrity structures with a large number of slack cables. These analyses are characterized by cables switching between taut and slack states and hence exhibit nonsmooth behaviors. The core concept is casting the original computation in each iteration step as a linear complementary problem. To deal with the geometric nonlinearity, the governing equation is formulated based on the positional formulation finite-element method, in which the nodal positions, rather than conventional nodal displacements, are adopted as generalized coordinates. By directly linearizing the governing equation, this complementarity framework is first used to study the static analysis in the small displacement regime and then extended to the large displacement case for both the static and dynamic analyses. Multiple examples are presented to demonstrate performances of the proposed complementarity framework in both the static and dynamic cases.